You certainly don't have to quit drag racing to autox....
That said, the two sports are only similar in that you are in a car, and trying to go for a quick time. Turning and launching want some very different chassis and suspension recations. We can make a car that handles well drag race pretty well, but you can't make a drag suspension turn very well.
I have folks on various sets meant to turn running in the 1.6-1.7 range on their 60's. No, it's not 1.5's, but then those cars can't pull 1g either.
SIK02SS is right, as you'll need to call me if I'm to help you as much as I can (there are things to discuss). I'd ask that before you call, you do two things. First, get a rulebook or download the SCCA rule book. At this point it seems to me you are in Street Mod already, but best to know how the rules work. And the other second thing, is thing about what's most important to you. I'm a handling guy, and I think you can use a good handing car's ability a lot more often, and everyday because it also makes the car drive better (not just turn faster). However, I'm not going to judge if you prefer the drag race thing, just remember that we can make the car leave still pretty well while making it turn. You just need to decide what the priority is and to what extent.
The Camaro I did for GMHTP magazine has a pretty basic handling setup on it, and one that has pulled 1.6 60's on other cars when on drag radials. On this car the suspension alone was good for about 3.4 seconds, and when sticky tires were added another 3.5 fell off the time on a 1.3 mile road course.